Load libraries

library(tidyverse) # data manipulation
library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data 
library(glmmTMB) # running generalised mixed models 
library(DHARMa) # model diagnostics 
library(performance) # model diagnostics  
library(ggeffects) # partial effect plots 
library(car) # running Anova on model 
library(emmeans) # post-hoc analysis

Import data

df_adults <- read_csv("import_data/resp_results_adults2.csv")
df_jresp <- read_csv("import_data/resp_results_juveniles.csv")

Data manipulation

Adults

df_adults_cleaned <- df_adults |> 
  mutate(FISH_ID = factor(FISH_ID), 
         Sex = factor(Sex), 
         Population = factor(Population), 
         Tank = factor(Tank), 
         Chamber = factor(Chamber), 
         System =factor(System), 
         Temperature =factor(Temperature), 
         True_resting=factor(True_resting)) 

df_males <- df_adults_cleaned |> 
  filter(Sex == "M")
df_females <- df_adults_cleaned |> 
  filter(Sex == "F")

df_adults_cleaned2 <- df_males |> 
  full_join(select(df_females, c("Tank","Temperature","Mass","Resting","Max","AAS","FISH_ID","Sex")), by="Tank") |> 
  mutate(Temperature.x = coalesce(Temperature.x, Temperature.y), 
         FISH_ID.x = coalesce(FISH_ID.x, FISH_ID.y),
         Sex.x = coalesce(Sex.x, Sex.y),
         Resting.midpoint = (Resting.x+Resting.y)/2, 
         Max.midpoint = (Max.x+Max.y)/2, 
         AAS.midpoint = (AAS.x+AAS.y)/2)

Juveniles

df_jresp$Population <-  fct_collapse(df_jresp$Population, 
                                      `Vlassof cay`= c("Vlassof reef", "Vlassof", "Vlassof Cay", "Vlassof cay"), 
                                      `Arlington reef` = c("Arlington reef","Arlginton reef")) 

#df_jresp$Female <-  fct_collapse(df_jresp$Female, 
                                  #`CARL359`= c("CARL359", "CARL59")) 


df_jresp2 <-  df_jresp |> 
  unite("F0", c("Male","Female"), sep="_", remove=FALSE) |>
  mutate(across(1:7, factor), 
         Temperature = factor(Temperature), 
         True_resting = factor(True_resting)) 

#df_jresp2_rest <- df_jresp2 |> 
  #filter(True_resting == "Y")

Merging dataframes

temp1a <- df_jresp2 |> 
  mutate(FISH_ID.x = Male)
temp1b <- df_jresp2 |> 
  mutate(FISH_ID.y = Female)
temp2a <- temp1a |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.x",
                                          "Sex.x",
                                          "Resting.x", 
                                          "Max.x", 
                                          "AAS.x", 
                                          "Mass.x")), 
                    by="FISH_ID.x")
temp2b <- temp1b |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.y",
                            "Sex.y",
                            "Resting.y", 
                            "Max.y", 
                            "AAS.y", 
                            "Mass.y")), 
                   by="FISH_ID.y") 
df_merged <- temp2a |> 
  left_join(select(temp2b, c("Clutch","Replicate", 
                             "FISH_ID.y",
                             "Resting.y", 
                             "Max.y", 
                             "AAS.y", 
                             "Mass.y")), 
            by=c("Clutch","Replicate"))
df <- df_merged |> 
  mutate(Resting_MALE =Resting.x, 
         Max_MALE =Max.x, 
         AAS_MALE =AAS.x, 
         Mass_MALE =Mass.x, 
         FISH_ID.y =FISH_ID.x,#makes more sense for males to be .y instead of .x
         FISH_ID.x =FISH_ID.x, 
         Resting_FEMALE =Resting.y, 
         Max_FEMALE =Max.y, 
         AAS_FEMALE =AAS.y, 
         Mass_FEMALE =Mass.y) |>  
  mutate(Max_MALE = Max_MALE/Mass_MALE, 
         Max_FEMALE =Max_FEMALE/Mass_FEMALE) |>
  mutate(Max_MID =(Max_MALE+Max_FEMALE)/2) |> # easier to do it again
  mutate(Max_MID =coalesce(Max_MID, Max_MALE)) |> 
  mutate(Max_MID =coalesce(Max_MID, Max_FEMALE)) |> 
  drop_na(Max) |> 
  group_by(Clutch) |> 
  mutate(MEDIAN_Max =median(Max_kg_wet)) |> 
  ungroup() |> 
  select(-c(Replicate, Chamber, System, Volume, Date_tested, Swim, Mass, Dry_mass, 18:26)) |> 
  distinct() |> 
  drop_na(Max_MID)

Exploratory analysis

Offspring-Male

plot <- ggplot(df, aes(x=Max_MALE, y=MEDIAN_Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'right')

plot

Offspring-Midpoint

plot <- ggplot(df, aes(x=Max_MID, y=MEDIAN_Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  ylab("Max (offspring)") + xlab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'right')
plot

Descriptive statistics

Juveniles - overview

Overview

tinytable_2prte3m3pw918azvhvoj
Population 27 28.5 30
Arlington reef 11 7 3
Pretty patches 5 3 5
Sudbury reef 5 2 2
Vlassof cay 5 0 5 
datasummary(Factor(F0) ~ Factor(Temperature), 
            data = df, 
            fmt = "%.0f")
tinytable_ouqxz4wkjgsoegydsh0i
F0 27 28.5 30
CARL217_CARL226 0 1 0
CARL218_CARL222 0 0 2
CARL230_CARL235 4 0 0
CARL233_CARL215 0 0 0
CARL237_CARL219 2 0 0
CARL241_CARL239 2 0 0
CARL249_CARL360 0 0 1
CARL335_CARL359 0 3 0
CARL338_CARL345 0 1 0
CARL344_CARL370 0 0 0
CARL354_CARL355 3 0 0
CARL360_CARL249 0 0 0
CARL367_CARL363 0 1 0
CARL369_CARL349 0 1 0
CPRE189_CPRE202 0 0 2
CPRE372_CPRE209 1 0 0
CPRE372_CPRE370 1 0 0
CPRE375_CPRE377 3 0 0
CPRE391_CPRE390 0 0 1
CPRE447_CPRE452 0 0 2
CPRE453_CPRE459 0 1 0
CPRE521_CPRE524 0 1 0
CPRE550_CPRE533 0 1 0
CSUD002_CSUD213 0 1 0
CSUD009_CSUD212 3 0 0
CSUD013_CSUD017 2 0 0
CSUD016_CSUD078 0 1 0
CSUD312_CSUD304 0 0 2
CVLA049_CVLA098 0 0 0
CVLA089_CVLA059 0 0 1
CVLA102_CVLA466 1 0 0
CVLA106_CVLA091 0 0 3
CVLA468_CVLA477 3 0 0
CVLA486_CVLA463 1 0 0
CVLA498_CVLA493 0 0 1

Juveniles

Maximum oxygen uptake

tinytable_ei890o4lb992eyobbzi1
Temperature NUnique mean median min max sd Histogram
27 21 926.01 922.96 742.12 1128.22 102.09 ▁▂▆▂▇▅▂▁▃
28.5 11 1059.28 1043.96 946.66 1211.16 86.34 ▅▂▇▂▅▂▅
30 14 1178.44 1146.47 916.48 1459.40 159.66 ▂▂▂▃▇▃▂▅

Adults - overview

Overview

datasummary(Factor(Population) ~ Factor(Temperature), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_hmkyymuhjdq7hqd5w7gl
Population 27 28.5 30
Arlington reef 8 7 4
Pretty patches 4 6 4
Sudbury reef 4 3 2
Vlassof cay 6 2 5 
datasummary(Factor(Population) ~ Factor(Temperature)*Factor(Sex), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_tlvnrvv41bgsasdx907e
27 28.5 30
Population F M F M F M
Arlington reef 4 4 2 5 2 2
Pretty patches 2 2 3 3 3 1
Sudbury reef 2 2 1 2 1 1
Vlassof cay 3 3 1 1 3 2

Pairs

datasummary(Factor(Population)*Factor(Temperature.x) ~ Max.x*(NUnique), 
            data = df_adults_cleaned2, 
            fmt = "%.0f")
tinytable_y7fvqzppuku2fbpjk78p
Population Temperature.x NUnique
Arlington reef 27 4
28.5 5
30 2
Pretty patches 27 2
28.5 3
30 1
Sudbury reef 27 2
28.5 2
30 1
Vlassof cay 27 3
28.5 1
30 2

Adults

Maximum oxygen uptake

tinytable_l9sfuh0bzrgu0scsumyv
Temperature NUnique mean median min max sd Histogram
27 22 16.58 16.91 9.70 22.06 3.36 ▃▃▅▅▃▃▅▇▂
28.5 18 17.09 17.23 11.04 28.39 3.94 ▅▂▅▇▇▃▂
30 12 16.80 17.35 11.78 21.24 3.03 ▂▅▂▇▂▂▅▂

Fit Models [random factors]

model1 <- glmmTMB(MEDIAN_Max ~ 1, 
                  family="gaussian",
                  data = df) 

model2 <- glmmTMB(MEDIAN_Max ~ (1|Population), 
                  family="gaussian",
                  data = df)
Model selection
AIC(model1, model2, k=2)
BIC(model1, model2)

Model1 performs the best therefore only Clutch will be used as a random factor in future models

Relationships

Offspring-Male

Fit model [fixed factors]

After figuring out which random factors will be incorporated into the model we will start to examine out fixed factors. Some fixed factors such as Max_(FE)MALE and TEMPERATURE will be essential to answering questions we have around heritability. Another factor that will be included is Dry_mass - which it should be pointed out in this experiment refers to the mass of fish after they were blotted dry with paper towel rather than completely dried out. Larger fish consume more oxygen, therefore, we need to account for this known relationship within our model. Out model will look something like this:

MEDIAN_Max ~ Max_MALE*Temprature

If we had alternative hypotheses to test would would do so at this stage. But in this instance the experiment was designed to answer a specific question via limiting potential covariates.

model1.1 <- glmmTMB(MEDIAN_Max ~ scale(Max_MALE)*Temperature, 
                    family=gaussian(), 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.064 0.22 0.548 0.088 0.248 0.12 0.16 0.116 0.136 0.476 0.408 0.744 0.344 0.276 0.584 0.568 0.628 0.66 0.464 0.988 ...
model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.093778, p-value = 0.8236
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0211, p-value = 0.816
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 0, observations = 45, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0000000 0.0787051
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                                      0
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.093778, p-value = 0.8236
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0211, p-value = 0.816
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 0, observations = 45, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0000000 0.0787051
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                                      0

performance

model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

model1.1 |> ggemmeans(~Max_MALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          MEDIAN_Max ~ scale(Max_MALE) * Temperature
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##    562.7    575.3   -274.3    548.7       38 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 1.16e+04 
## 
## Conditional model:
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                      928.472     26.418   35.15  < 2e-16 ***
## scale(Max_MALE)                    5.018     32.491    0.15 0.877255    
## Temperature28.5                  142.592     41.699    3.42 0.000627 ***
## Temperature30                    296.210    128.042    2.31 0.020701 *  
## scale(Max_MALE):Temperature28.5  -46.463     44.978   -1.03 0.301598    
## scale(Max_MALE):Temperature30    -17.517     94.662   -0.19 0.853189    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

model1.1 |> Anova()

confint

model1.1 |> confint()
##                                      2.5 %    97.5 %   Estimate
## (Intercept)                      876.69439 980.24979 928.472088
## scale(Max_MALE)                  -58.66269  68.69915   5.018226
## Temperature28.5                   60.86327 224.32114 142.592206
## Temperature30                     45.25298 547.16674 296.209861
## scale(Max_MALE):Temperature28.5 -134.61959  41.69285 -46.463373
## scale(Max_MALE):Temperature30   -203.05049 168.01613 -17.517180

r-squared

model1.1 |> r2_nakagawa()
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.499

Pairwise comparisons

emmeans [Temperature]

model1.1 |> emmeans(pairwise ~ Temperature, type="response") |> 
  summary(by=NULL, adjust="sidak", infer=TRUE)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
##  Temperature emmean    SE df lower.CL upper.CL t.ratio p.value
##  27             928  26.4 38      862      994  35.146  <.0001
##  28.5          1071  32.3 38      990     1152  33.197  <.0001
##  30            1225 125.3 38      912     1538   9.775  <.0001
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests 
## 
## $contrasts
##  contrast                        estimate    SE df lower.CL upper.CL t.ratio
##  Temperature27 - Temperature28.5     -143  41.7 38     -247    -38.4  -3.420
##  Temperature27 - Temperature30       -296 128.0 38     -616     23.6  -2.313
##  Temperature28.5 - Temperature30     -154 129.4 38     -477    169.5  -1.187
##  p.value
##   0.0045
##   0.0766
##   0.5652
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests

Summary figure

om.max <- emmeans(model1.1, ~Max_MALE*Temperature, 
                   at =list(Max_MALE =seq(from=300, to =550, by=5)))

om.max.df <- as.data.frame(om.max)

om.max.obs <- drop_na(df, Max_MALE, MEDIAN_Max) |> 
  mutate(Pred =predict(model1.1, re.form =NA, type='response'), 
         Resid =residuals(model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.max.obs.summarize <- om.max.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.max =mean(Fit, na.rm=TRUE),
            mean.max_male =mean(Max_MALE, na.rm=TRUE),
            sd.max =sd(Fit, na.rm =TRUE), 
            n.max = n()) |> 
  mutate(se.max = sd.max / sqrt(n.max), 
         lower.ci.max =mean.max - qt(1 - (0.05/2), n.max -1) * se.max, 
         upper.ci.max =mean.max + qt(1 - (0.05/2), n.max - 1) * se.max)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
## Warning: There were 62 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.max = mean.max - qt(1 - (0.05/2), n.max - 1) *
##   se.max`.
## ℹ In group 1: `Clutch = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 61 remaining warnings.
ggplot(data =om.max.df, aes(y=emmean, x=Max_MALE)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.max.obs.summarize, aes(y =mean.max, x=mean.max_male, 
                                                    ymin =lower.ci.max, 
                                                    ymax =upper.ci.max, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 16 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_segment()`).

Offspring-midpoint

Fit model [fixed factors]

mid_model1.1 <- glmmTMB(MEDIAN_Max ~ scale(Max_MID)*Temperature, 
                    family=gaussian(), 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

mid_model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.044 0.18 0.572 0.196 0.108 0.3 0.252 0.148 0 0.112 0.18 0.176 0.472 0.448 0.772 0.528 0.38 0.4 0.56 0.636 ...
mid_model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.10725, p-value = 0.5757
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0199, p-value = 0.824
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 1, observations = 53, p-value = 0.3456
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0004775804 0.1007015268
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01886792
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.10725, p-value = 0.5757
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0199, p-value = 0.824
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 1, observations = 53, p-value = 0.3456
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0004775804 0.1007015268
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01886792

performance

mid_model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

mid_model1.1 |> ggemmeans(~Max_MID|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

mid_model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          MEDIAN_Max ~ scale(Max_MID) * Temperature
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##    665.4    679.2   -325.7    651.4       46 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 1.27e+04 
## 
## Conditional model:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     930.561     23.792   39.11  < 2e-16 ***
## scale(Max_MID)                   12.824     24.658    0.52  0.60301    
## Temperature28.5                 133.571     40.524    3.30  0.00098 ***
## Temperature30                   243.039     42.467    5.72 1.05e-08 ***
## scale(Max_MID):Temperature28.5  -49.182     37.955   -1.30  0.19505    
## scale(Max_MID):Temperature30     -3.299     46.033   -0.07  0.94286    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

mid_model1.1 |> Anova()

confint

mid_model1.1 |> confint()
##                                     2.5 %    97.5 %   Estimate
## (Intercept)                     883.92997 977.19288 930.561420
## scale(Max_MID)                  -35.50429  61.15177  12.823740
## Temperature28.5                  54.14541 212.99604 133.570727
## Temperature30                   159.80482 326.27245 243.038635
## scale(Max_MID):Temperature28.5 -123.57303  25.20887 -49.182078
## scale(Max_MID):Temperature30    -93.52175  86.92327  -3.299244

r-squared

mid_model1.1 |> r2_nakagawa()
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.494

Summary figure

om.max <- emmeans(mid_model1.1, ~Max_MID*Temperature, 
                   at =list(Max_MID =seq(from=300, to =600, by=5)))

om.max.df <- as.data.frame(om.max)

om.max.obs <- drop_na(df, Max_MID, MEDIAN_Max) |> 
  mutate(Pred =predict(mid_model1.1, re.form =NA, type='response'), 
         Resid =residuals(mid_model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.max.obs.summarize <- om.max.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.max =mean(Fit, na.rm=TRUE),
            mean.max_female =mean(Max_MID, na.rm=TRUE),
            sd.max =sd(Fit, na.rm =TRUE), 
            n.max = n()) |> 
  mutate(se.max = sd.max / sqrt(n.max), 
         lower.ci.max =mean.max - qt(1 - (0.05/2), n.max -1) * se.max, 
         upper.ci.max =mean.max + qt(1 - (0.05/2), n.max - 1) * se.max)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
## Warning: There were 78 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.max = mean.max - qt(1 - (0.05/2), n.max - 1) *
##   se.max`.
## ℹ In group 1: `Clutch = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 77 remaining warnings.
ggplot(data =om.max.df, aes(y=emmean, x=Max_MID)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.max.obs.summarize, aes(y =mean.max, x=mean.max_female, 
                                                    ymin =lower.ci.max, 
                                                    ymax =upper.ci.max, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 16 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 13 rows containing missing values or values outside the scale range
## (`geom_segment()`).